Related papers: An adaptive POD approximation method for the contr…
In this paper we extend dynamic programming techniques to the study of discrete-time infinite horizon optimal control problems on compact control invariant sets with state-independent best asymptotic average cost. To this end we analyse the…
Variational data assimilation technique applied to identification of optimal approximations of derivatives near boundary is discussed in frames of one-dimensional wave equation. Simplicity of the equation and of its numerical scheme allows…
This paper deals with a stochastic recursive optimal control problem, where the diffusion coefficient depends on the control variable and the control domain is not necessarily convex. We focus on the connection between the general maximum…
In this paper we present a new algorithm for the solution of Hamilton-Jacobi-Bellman equations related to optimal control problems. The key idea is to divide the domain of computation into subdomains which are shaped by the optimal dynamics…
This paper develops a comprehensive Hamilton-Jacobi framework to analyze asymptotic propagation dynamics in a field-road system featuring unidirectional advection and Wentzell-type boundary conditions. We rigorously derive a Hamilton-Jacobi…
This paper is concerned with a discounted stochastic optimal control problem for regime switching diffusion in an infinite horizon. First, as a preliminary with particular interests in its own right, the global well-posedness of infinite…
Motivated by the design of fast reinforcement learning algorithms, we study the diffusive limit of a class of pure jump ergodic stochastic control problems. We show that, whenever the intensity of jumps is large enough, the approximation…
This paper presents a novel adaptive-sparse polynomial dimensional decomposition (PDD) method for stochastic design optimization of complex systems. The method entails an adaptive-sparse PDD approximation of a high-dimensional stochastic…
Adapting pretrained diffusion models to downstream objectives such as inverse problems often requires expensive test-time guidance or optimization. We propose a principled framework for generating high-quality reward-aligned samples at…
We investigate the long time behavior of weakly dissipative semilinear Hamilton-Jacobi-Bellman (HJB) equations and the turnpike property for the corresponding stochastic control problems. To this aim, we develop a probabilistic approach…
We develop algorithms that find and track the optimal solution trajectory of time-varying convex optimization problems which consist of local and network-related objectives. The algorithms are derived from the prediction-correction…
We propose a time-adaptive predictor/multi-corrector method to solve hyperbolic partial differential equations, based on the generalized-$\alpha$ scheme that provides user-control on the numerical dissipation and second-order accuracy in…
In our previous work [Singler, SIAM J. Numer. Anal. 52 (2014), no. 2, 852-876], we considered the proper orthogonal decomposition (POD) of time varying PDE solution data taking values in two different Hilbert spaces. We considered various…
In this paper, we propose high order numerical methods to solve a 2D advection diffusion equation, in the highly oscillatory regime. We use an integrator strategy that allows the construction of arbitrary high-order schemes {leading} to an…
In this paper, we propose an iterative convolution-thresholding method (ICTM) based on prediction-correction for solving the topology optimization problem in steady-state heat transfer equations. The problem is formulated as a constrained…
We consider continuous-state and continuous-time control problems where the admissible trajectories of the system are constrained to remain on a union of half-planes which share a common straight line. This set will be named a junction. We…
This paper presents the design and analysis of a Hybrid High-Order (HHO) approximation for a distributed optimal control problem governed by the Poisson equation. We propose three distinct schemes to address unconstrained control problems…
In the present work we study the optimal control of an evolution equation with non-smooth dissipation. The solution mapping of this system is non-smooth and hence the analysis is quite challenging. Our approach is to regularize the…
In this paper, we study the numerical approximation of a system of PDEs with fractional time derivatives. This system is derived from an optimal control problem for a time-fractional Fokker-Planck equation with time dependent drift by…
We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…